Finite Group Databasebeta

← C2×#22620624 #33955890

Subgroups — C2×#22620624 #33955890

Order 18688.

2278 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989132C211yesmaximal, characteristic, complemented
2C2×#17989118C211yesmaximal, characteristic, complemented
3#22620624C2116yesmaximal, direct product factor
4C2×#17988995C211yesmaximal, characteristic, complemented
5C2×#17988975C211yesmaximal, characteristic, complemented
6C2×#17988950C211yesmaximal, characteristic, complemented
7C2×#17988945C211yesmaximal, characteristic, complemented
8C2×#17988821C211yesmaximal, characteristic, complemented
9C2×#17988816C211yesmaximal, characteristic, complemented
10C2×#17988814C211yesmaximal, characteristic, complemented
11C2×#17988699C211yesmaximal, characteristic, complemented
12C2×#17988696C211yesmaximal, characteristic, complemented
13C2×#17988686C211yesmaximal, characteristic, complemented
14C2×#17988684C211yesmaximal, characteristic, complemented
15C22×#14556501C211yesmaximal, characteristic, complemented
16C2×#466×C73C211yesmaximal, characteristic, complemented
17C22×#11924027—21no—
18C22×#11924017C2211yescharacteristic
19C22×#11924016C2211yescharacteristic
20C22×#11924013C2211yescharacteristic
21C23×#10596831C2211yescharacteristic
22#17989132—24no—
23#17989132C2218yescomplemented
24C2×#14556590C2211yescharacteristic
25C2×#14556587C2211yescharacteristic
26#17989118—24no—
27#17989118C2218yescomplemented
28C2×#14556584—21no—
29C2×#14556582C2211yescharacteristic
30C2×#14556578C2211yescharacteristic
31C2×#14556577—21no—
32C2×#14556572—21no—
33C2×#14556570C2211yescharacteristic
34C2×#14556565C2211yescharacteristic
35C2×#14556563—21no—
36C2×#14556556C2211yescharacteristic
37C2×D4×Dic73—21no—
38C2×D4×Dic73C2211yescharacteristic
39C2×D4×Dic73C2211yescharacteristic
40C2×#14556553C2211yescharacteristic
41C2×#14556551—21no—
42C2×#14556547—21no—
43C22×C4×Dic73C2211yescharacteristic
44#17988995C2218yescomplemented
45#17988975C2218yescomplemented
46#17988950C2218yescomplemented
47#17988945C2218yescomplemented
48#17988821C2218yescomplemented
49#17988816C2218yescomplemented
50#17988814C2218yescomplemented
51#17988699C2218yescomplemented
52#17988696C2218yescomplemented
53#17988686C2218yescomplemented
54#17988684C2218yescomplemented
55C2×#14556524C2211yescharacteristic
56C2×#14556523C2211yescharacteristic
57C2×#14556522C2211yescharacteristic
58C2×#14556516C2211yescharacteristic
59C2×#14556514C2211yescharacteristic
60C2×#14556513C2211yescharacteristic
61C2×#14556512C2211yescharacteristic
62C2×#14556512C2211yescharacteristic
63C2×#14556511C2211yescharacteristic
64C2×#14556501C2211yescharacteristic
65C2×#14556501C2211yescharacteristic
66C2×#14556501C2211yescharacteristic
67C2×#14556501C2211yescharacteristic
68C2×#14556501C2218yescomplemented
69C22×D8×C73C2211yescharacteristic
70C23×C8×C73C2211yescharacteristic
71C2×#121×C73C2211yescharacteristic
72C2×#121×C73C2211yescharacteristic
73#466×C73C2218yescomplemented
74C2×#107×C73C2211yescharacteristic
75C2×#102×C73C2211yescharacteristic
76C2×#102×C73C2211yescharacteristic
77C2×#11924027—28no—
78C2×#11924027—48no—
79C22×Dic146—21no—
80C22×Dic146C2311yescharacteristic
81C22×D292C2311yescharacteristic
82C22×C22⋊D73—21no—
83C22×C22⋊D73—21no—
84C22×C22⋊D73—21no—
85C23×Dic73—21no—
86C23×Dic73—21no—
87C23×Dic73D411yescharacteristic
88C23×Dic73D411yescharacteristic
89C22×C4×D73—21no—
90C2×#11924017—24no—
91C2×#11924017C2314yes—
92C2×#11924016—24no—
93C2×#11924016C2314yes—
94C2×#11924013—24no—
95C2×#11924013C2314yes—
96C22×#10596831—24no—
97C22×#10596831C2311yescharacteristic
98C22×#10596831C2314yes—
99C22×#10596831C2311yescharacteristic
100#14556590—22no—
101#14556590C2314yes—
102#14556587—22no—
103#14556587C2314yes—
104#14556584—28no—
105#14556582—22no—
106#14556582C2314yes—
107#14556578—22no—
108#14556578C2314yes—
109#14556577—28no—
110#14556572—28no—
111#14556570—22no—
112#14556570C2314yes—
113#14556565—22no—
114#14556565C2314yes—
115#14556563—28no—
116#14556556—22no—
117#14556556C2314yes—
118D4×Dic73—28no—
119D4×Dic73—22no—
120D4×Dic73—22no—
121D4×Dic73C2314yes—
122D4×Dic73C2314yes—
123#14556553—22no—
124#14556553C2314yes—
125#14556551—28no—
126#14556547—28no—
127C2×C4⋊Dic73—21no—
128C2×C4⋊Dic73C2311yescharacteristic
129C2×C4⋊Dic73C2311yescharacteristic
130C2×#11924007—21no—
131C2×#11924007—21no—
132C2×#11924007—21no—
133C2×#11924007—21no—
134C2×C22⋊Dic73—21no—
135C2×C22⋊Dic73—21no—
136C2×C22⋊Dic73—21no—
137C2×C22⋊Dic73—21no—
138C2×C22⋊Dic73—21no—
139C2×#11924005—21no—
140C2×#11924005—21no—
141C2×C4×Dic73—21no—
142C2×C4×Dic73D414yes—
143C2×C4×Dic73D411yescharacteristic
144C2×C4×Dic73D411yescharacteristic
145C2×C4×Dic73C2311yescharacteristic
146C2×C4×Dic73C2314yes—
147C2×C4×Dic73C2311yescharacteristic
148#14556524C2314yes—
149#14556523C2314yes—
150#14556522C2314yes—
151#14556516C2314yes—
152#14556514C2314yes—
153#14556513C2314yes—
154#14556512C2314yes—
155#14556512C2314yes—
156#14556511C2314yes—
157#14556501C2314yes—
158#14556501C2314yes—
159#14556501C2314yes—
160#14556501C2314yes—
161C22×D4×C73—21no—
162C22×D4×C73—21no—
163C22×D4×C73C2311yescharacteristic
164C22×D4×C73C2311yescharacteristic
165C23×C4×C73C2311yescharacteristic
166C2×D8×C73—24no—
167C2×D8×C73C2314yes—
168C22×C8×C73—24no—
169C22×C8×C73C2311yescharacteristic
170C22×C8×C73C2314yes—
171C22×C8×C73C2311yescharacteristic
172#121×C73—22no—
173#121×C73—22no—
174#121×C73C2314yes—
175#121×C73C2314yes—
176C2×C4⋊C4×C73C2311yescharacteristic
177C2×C4⋊C4×C73C2311yescharacteristic
178C2×C22⋊C4×C73—21no—
179C2×C22⋊C4×C73—21no—
180#107×C73C2314yes—
181#102×C73C2314yes—
182#102×C73C2314yes—
183C23×D73—21no—
184#11924027—432no—
185C2×Dic146—22no—
186C2×Dic146—22no—
187C2×Dic146—21no—
188C2×Dic146—24no—
189C2×Dic146—44no—
190C2×Dic146C2412yes—
191C2×D292—22no—
192C2×D292—22no—
193C2×D292—21no—
194C2×D292C2412yes—
195C2×C22⋊D73—24no—
196C2×C22⋊D73—24no—
197C2×C22⋊D73—24no—
198C2×C22⋊D73—44no—
199C2×C22⋊D73—44no—
200C2×C22⋊D73—44no—
201C22×Dic73—24no—
202C22×Dic73—21no—
203C22×Dic73—21no—
204C22×Dic73—21no—
205C22×Dic73—24no—
206C22×Dic73—24no—
207C22×Dic73—42no—
208C22×Dic73—44no—
209C22×Dic73—44no—
210C22×Dic73C2×D411yescharacteristic
211C22×Dic73C2×D411yescharacteristic
212C22×Dic73C2×D411yescharacteristic
213C22×Dic73C2×D411yescharacteristic
214C22×Dic73C2×D414yes—
215C22×Dic73C2×D414yes—
216C2×C4×D73—24no—
217C2×C4×D73—44no—
218#11924017—28no—
219#11924016—28no—
220#11924013—28no—
221C2×#10596831—22no—
222C2×#10596831—28no—
223C2×#10596831#4114yescomplemented
224C2×#10596831C2412yes—
225C2×#10596831C2412yes—
226C4⋊Dic73—21no—
227C4⋊Dic73—21no—
228C4⋊Dic73—24no—
229C4⋊Dic73C2412yes—
230C4⋊Dic73C2412yes—
231#11924007—24no—
232#11924007—24no—
233#11924007—24no—
234#11924007—24no—
235C22⋊Dic73—24no—
236C22⋊Dic73—24no—
237C22⋊Dic73—24no—
238C22⋊Dic73—24no—
239C22⋊Dic73—24no—
240#11924005—24no—
241#11924005—24no—
242C4×Dic73—24no—
243C4×Dic73C2×D414yes—
244C4×Dic73C2×D414yes—
245C4×Dic73C2×D412yes—
246C4×Dic73C2×D412yes—
247C4×Dic73C2412yes—
248C4×Dic73C2412yes—
249C24×C73—21no—
250C24×C73—21no—
251C24×C73C2×D411yescharacteristic
252C2×D4×C73—24no—
253C2×D4×C73—24no—
254C2×D4×C73—21no—
255C2×D4×C73—21no—
256C2×D4×C73—22no—
257C2×D4×C73—22no—
258C2×D4×C73—22no—
259C2×D4×C73—22no—
260C2×D4×C73—44no—
261C2×D4×C73—44no—
262C2×D4×C73C2412yes—
263C2×D4×C73C2412yes—
264C22×C4×C73—22no—
265C22×C4×C73—22no—
266C22×C4×C73—21no—
267C22×C4×C73—21no—
268C22×C4×C73C2×D411yescharacteristic
269C22×C4×C73C2×D412yes—
270C22×C4×C73C2412yes—
271C22×C4×C73C2411yescharacteristic
272D8×C73—28no—
273C2×C8×C73—22no—
274C2×C8×C73—28no—
275C2×C8×C73#4114yescomplemented
276C2×C8×C73C2412yes—
277C2×C8×C73C2412yes—
278C4⋊C4×C73—21no—
279C4⋊C4×C73—21no—
280C4⋊C4×C73C2412yes—
281C4⋊C4×C73C2412yes—
282C22⋊C4×C73—24no—
283C22⋊C4×C73—24no—
284C23×C73—22no—
285C23×C73—22no—
286C23×C73—22no—
287C23×C73—22no—
288C23×C73—42no—
289C23×C73—42no—
290C23×C73—42no—
291C23×C73—42no—
292C23×C73—42no—
293C23×C73—42no—
294C23×C73AGL(1,ℤ/8)14yes—
295C23×C73C22×D412yes—
296C23×C73C22×D411yescharacteristic
297C22×D73—22no—
298C22×D73—42no—
299C22×D73—42no—
300C22×D73—42no—
301D4×C73—22no—
302D4×C73—22no—
303D4×C73—22no—
304D4×C73—22no—
305D4×C73—48no—
306D4×C73—48no—
307D4×C73—42no—
308D4×C73—42no—
309C2×C4×C73—22no—
310C2×C4×C73—24no—
311C2×C4×C73—22no—
312C2×C4×C73—22no—
313C2×C4×C73—22no—
314C2×C4×C73—22no—
315C2×C4×C73—42no—
316C2×C4×C73—42no—
317C2×C4×C73C22×D412yes—
318C2×C4×C73C22×D411yescharacteristic
319C2×C4×C73C2×#4112yes—
320C2×C4×C73C2×#4112yes—
321C2×C4×C73C2511yescharacteristic
322C22⋊D73—48no—
323C22⋊D73—48no—
324C22⋊D73—48no—
325C2×Dic73—22no—
326C2×Dic73—22no—
327C2×Dic73—28no—
328C2×Dic73—22no—
329C2×Dic73—22no—
330C2×Dic73—22no—
331C2×Dic73—22no—
332C2×Dic73—22no—
333C2×Dic73—44no—
334C2×Dic73—48no—
335C2×Dic73—48no—
336C2×Dic73—42no—
337C2×Dic73—42no—
338C2×Dic73—42no—
339C2×Dic73C22×D412yes—
340C2×Dic73C22×D412yes—
341C2×Dic73C22×D412yes—
342C2×Dic73C22×D412yes—
343D292—22no—
344D292—22no—
345D292—42no—
346C4×D73—48no—
347Dic146—22no—
348Dic146—22no—
349Dic146—48no—
350Dic146—42no—
351C8×C73—22no—
352C8×C73C2×#4114yescomplemented
353#10596831—22no—
354#10596831C2×#4114yescomplemented
355C22×C73—28no—
356C22×C73—22no—
357C22×C73—22no—
358C22×C73—42no—
359C22×C73—42no—
360C22×C73—42no—
361C22×C73—42no—
362C22×C73—42no—
363C22×C73—42no—
364C22×C73—84no—
365C22×C73—84no—
366C22×C73#53212yes—
367C22×C73C2×AGL(1,ℤ/8)14yes—
368C22×C73C2×AGL(1,ℤ/8)12yes—
369C22×C73#57512yes—
370C22×C73C23×D411yescharacteristic
371C2×D73—42no—
372C2×D73—42no—
373C2×D73—42no—
374C2×D73—84no—
375C4×C73—22no—
376C4×C73—42no—
377C4×C73—42no—
378C4×C73#53212yes—
379C4×C73C22×#4111yescharacteristic
380C4×C73C22×#4111yescharacteristic
381Dic73—22no—
382Dic73—22no—
383Dic73—22no—
384Dic73—22no—
385Dic73—42no—
386Dic73—42no—
387Dic73—42no—
388C2×#3180—731nomaximal, Sylow
389C2×C73—24no—
390C2×C73—82no—
391C2×C73—82no—
392C2×C73#318014yescomplemented
393C2×C73C2×#53211yescharacteristic
394C2×C73C22×AGL(1,ℤ/8)11yescharacteristic
395C2×C73C2×#57511yescharacteristic
396D73—82no—
397C2×#532—731no—
398C2×#529—731no—
399#3180—7316no—
400C2×#501—731no—
401C2×#496—731no—
402C2×#490—731no—
403C2×#489—731no—
404C2×#466—731no—
405C2×#466D7311yescharacteristic, complemented
406C2×#465—731no—
407C2×#465—731no—
408C2×#442—731no—
409C2×#442—731no—
410C2×#440—731no—
411C2×#440—731no—
412C22×#97—731no—
413C73C2×#318011yescharacteristic, complemented, Sylow
414C22×#41—1461no—
415C22×SD16—731no—
416C22×SD16—731no—
417C22×D8—731no—
418C22×D8C2×D7311yescharacteristic
419C23×C8—731no—
420C23×C8C2×D7311yescharacteristic
421#532—738no—
422#532—1464no—
423C2×C4⋊Q8—731no—
424C2×#127—731no—
425#529—738no—
426#529—1464no—
427C2×#126—1461no—
428C2×#125—731no—
429C2×#124—731no—
430C2×#124—1461no—
431C2×#123—1461no—
432C2×C22⋊Q8—731no—
433C2×#121—731no—
434C2×#121—1461no—
435C2×#121C2×D7311yescharacteristic
436C2×#121C2×D7311yescharacteristic
437C2×C4×Q8—731no—
438C2×C4×D4—731no—
439C2×C4×D4—731no—
440C2×C4×D4—731no—
441C2×C4×D4—1461no—
442C2×C4×D4—1461no—
443C2×#117—1461no—
444C22×C42—731no—
445#501—738no—
446#496—738no—
447#490—738no—
448#489—738no—
449#466—738no—
450#466C2×D7318yescomplemented
451#465—738no—
452#465—738no—
453#442—738no—
454#442—738no—
455#440—738no—
456#440—738no—
457C2×#107—731no—
458C2×#107C2×D7311yescharacteristic
459C2×#106—731no—
460C2×#106—731no—
461C2×#103—731no—
462C2×#103—731no—
463C2×#102—731no—
464C2×#102—731no—
465C2×#102—731no—
466C2×#102—731no—
467C2×#102C2×D7311yescharacteristic
468C2×#102C2×D7311yescharacteristic
469C2×#97—731no—
470C2×#97—731no—
471C2×#97—738no—
472C2×#97—731no—
473C2×#97—731no—
474C2×#41—2928no—
475C2×#41—1468no—
476C22×Q8—731no—
477C22×Q8—1461no—
478C22×D4—21no—
479C22×D4—21no—
480C22×D4—731no—
481C22×D4—1461no—
482C22×D4—1461no—
483C22×D4—1461no—
484C22×D4C22×D7311yescharacteristic
485C22×D4C22×D7311yescharacteristic
486C23×C4—731no—
487C23×C4—731no—
488C23×C4—1461no—
489C23×C4—1461no—
490C23×C4—1461no—
491C23×C4C22×D7311yescharacteristic
492C2×SD16—734no—
493C2×SD16—734no—
494C2×SD16—1464no—
495C2×SD16—1464no—
496C2×D8—24no—
497C2×D8—734no—
498C2×D8—1464no—
499C2×D8C22×D7314yes—
500C22×C8—24no—
501C22×C8—731no—
502C22×C8—731no—
503C22×C8—734no—
504C22×C8—1464no—
505C22×C8C22×D7311yescharacteristic
506C22×C8C22×D7314yes—
507C22×C8C22×D7311yescharacteristic
508C4⋊Q8—734no—
509C4⋊Q8—1462no—
510#127—734no—
511#127—1462no—
512#126—1468no—
513#125—734no—
514#125—1462no—
515#124—734no—
516#124—1468no—
517#124—1462no—
518#123—1468no—
519C22⋊Q8—734no—
520C22⋊Q8—1462no—
521#121—22no—
522#121—22no—
523#121—734no—
524#121—1468no—
525#121—1462no—
526#121C22×D7314yes—
527#121C22×D7314yes—
528C4×Q8—734no—
529C4×Q8—1462no—
530C4×D4—734no—
531C4×D4—734no—
532C4×D4—734no—
533C4×D4—1468no—
534C4×D4—1462no—
535C4×D4—1462no—
536C4×D4—1462no—
537C4×D4—1468no—
538#117—1468no—
539C2×C4⋊C4—731no—
540C2×C4⋊C4—731no—
541C2×C4⋊C4—1461no—
542C2×C4⋊C4—1461no—
543C2×C4⋊C4—1461no—
544C2×C4⋊C4—1461no—
545C2×C4⋊C4—1461no—
546C2×C4⋊C4C22×D7311yescharacteristic
547C2×C4⋊C4C22×D7311yescharacteristic
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—1461no—
551C2×C22⋊C4—1461no—
552C2×C22⋊C4—1461no—
553C2×C22⋊C4—1461no—
554C2×C22⋊C4—1461no—
555C2×C22⋊C4—1461no—
556C2×C22⋊C4—1461no—
557C2×C42—731no—
558C2×C42—731no—
559C2×C42—734no—
560C2×C42—731no—
561C2×C42—731no—
562C2×C42—734no—
563C2×C42—1461no—
564#107—734no—
565#107C22×D7314yes—
566#106—734no—
567#106—734no—
568#103—734no—
569#103—734no—
570#102—734no—
571#102—734no—
572#102—734no—
573#102—734no—
574#102C22×D7314yes—
575#102C22×D7314yes—
576#97—734no—
577#97—734no—
578#97—734no—
579#97—734no—
580C24—21no—
581C24—21no—
582C24—1461no—
583C24D4×D7311yescharacteristic
584#41—29232no—
585C2×Q8—2924no—
586C2×Q8—732no—
587C2×Q8—1464no—
588C2×Q8—1462no—
589C2×Q8—1462no—
590C2×Q8—1461no—
591C2×D4—24no—
592C2×D4—24no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—44no—
600C2×D4—44no—
601C2×D4—2924no—
602C2×D4—2924no—
603C2×D4—2924no—
604C2×D4—732no—
605C2×D4—1464no—
606C2×D4—1464no—
607C2×D4—1464no—
608C2×D4—1461no—
609C2×D4—1462no—
610C2×D4—1462no—
611C2×D4C23×D7312yes—
612C2×D4C23×D7312yes—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—2924no—
618C22×C4—2924no—
619C22×C4—2924no—
620C22×C4—2922no—
621C22×C4—734no—
622C22×C4—734no—
623C22×C4—731no—
624C22×C4—731no—
625C22×C4—731no—
626C22×C4—731no—
627C22×C4—1464no—
628C22×C4—1464no—
629C22×C4—1464no—
630C22×C4—1461no—
631C22×C4—1461no—
632C22×C4—1461no—
633C22×C4—1464no—
634C22×C4D4×D7312yes—
635C22×C4D4×D7311yescharacteristic
636C22×C4C23×D7312yes—
637C22×C4C23×D7311yescharacteristic
638SD16—1468no—
639SD16—1468no—
640D8—28no—
641D8—1468no—
642C2×C8—22no—
643C2×C8—28no—
644C2×C8—734no—
645C2×C8—732no—
646C2×C8—732no—
647C2×C8—1468no—
648C2×C8—1462no—
649C2×C8#1192402714yescomplemented
650C2×C8C23×D7312yes—
651C2×C8C23×D7312yes—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—732no—
655C4⋊C4—732no—
656C4⋊C4—1464no—
657C4⋊C4—1464no—
658C4⋊C4—1464no—
659C4⋊C4—1464no—
660C4⋊C4—1464no—
661C4⋊C4—1461no—
662C4⋊C4—1461no—
663C4⋊C4C23×D7312yes—
664C4⋊C4C23×D7312yes—
665C22⋊C4—24no—
666C22⋊C4—24no—
667C22⋊C4—1464no—
668C22⋊C4—1464no—
669C22⋊C4—1464no—
670C22⋊C4—1464no—
671C22⋊C4—1464no—
672C22⋊C4—1464no—
673C22⋊C4—1464no—
674C42—734no—
675C42—732no—
676C42—734no—
677C42—732no—
678C42—732no—
679C42—732no—
680C42—1464no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—2922no—
692C23—2922no—
693C23—2922no—
694C23—1462no—
695C23#1455661514yes—
696C23C2×D4×D7312yes—
697C23C2×D4×D7311yescharacteristic
698Q8—2928no—
699Q8—2922no—
700Q8—1462no—
701Q8—1462no—
702D4—22no—
703D4—22no—
704D4—22no—
705D4—22no—
706D4—48no—
707D4—48no—
708D4—42no—
709D4—42no—
710D4—2928no—
711D4—2928no—
712D4—2928no—
713D4—2922no—
714D4—1462no—
715D4—1462no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—2928no—
725C2×C4—2922no—
726C2×C4—2922no—
727C2×C4—2922no—
728C2×C4—2928no—
729C2×C4—2928no—
730C2×C4—2924no—
731C2×C4—732no—
732C2×C4—732no—
733C2×C4—732no—
734C2×C4—732no—
735C2×C4—1462no—
736C2×C4—1462no—
737C2×C4—1462no—
738C2×C4—1462no—
739C2×C4—1462no—
740C2×C4—1462no—
741C2×C4—1462no—
742C2×C4—1468no—
743C2×C4C2×D4×D7312yes—
744C2×C4C2×D4×D7311yescharacteristic
745C2×C4#41×D7312yes—
746C2×C4C2×#1192402712yes—
747C2×C4C24×D7311yescharacteristic
748C8—22no—
749C8—734no—
750C8—1462no—
751C8C2×#1192402714yescomplemented
752C22—22no—
753C22—28no—
754C22—22no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—84no—
762C22—84no—
763C22—2922no—
764C22—2922no—
765C22—2922no—
766C22—5844no—
767C22#1798913212yes—
768C22C2×#1455661514yes—
769C22C2×#1455661512yes—
770C22#1798938412yes—
771C22C22×D4×D7311yescharacteristic
772C4—22no—
773C4—42no—
774C4—42no—
775C4—2922no—
776C4—2922no—
777C4—2922no—
778C4—1462no—
779C4—1462no—
780C4—1462no—
781C4—1462no—
782C4#1798913212yes—
783C4C2×#41×D7311yescharacteristic
784C4C22×#1192402711yescharacteristic
785C2—24no—
786C2—82no—
787C2—82no—
788C2—5842no—
789C2#2262062414yesdirect product factor
790C2C2×#1798913211yescharacteristic
791C2C22×#1455661511yescharacteristic
792C2C2×#1798938411yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#466×C73C2
socleC23×C73C22×D4
hypercenterC2×#466D73
hypocenterC73C2×#3180
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#466

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#17989132C2semidirect
2. C2×#17989118C2semidirect
3. #22620624C2direct (N × H)
4. C2×#17988995C2semidirect
5. C2×#17988975C2semidirect
6. C2×#17988950C2semidirect
7. C2×#17988945C2semidirect
8. C2×#17988821C2semidirect
9. C2×#17988816C2semidirect
10. C2×#17988814C2semidirect
11. C2×#17988699C2semidirect
12. C2×#17988696C2semidirect
13. C2×#17988686C2semidirect
14. C2×#17988684C2semidirect
15. C22×#14556501C2semidirect
16. C2×#466×C73C2semidirect
23. #17989132C22semidirect
27. #17989118C22semidirect
44. #17988995C22semidirect
45. #17988975C22semidirect
46. #17988950C22semidirect
47. #17988945C22semidirect
48. #17988821C22semidirect
49. #17988816C22semidirect
50. #17988814C22semidirect
51. #17988699C22semidirect
52. #17988696C22semidirect
53. #17988686C22semidirect
54. #17988684C22semidirect
68. C2×#14556501C22semidirect
73. #466×C73C22semidirect
223. C2×#10596831#41semidirect
275. C2×C8×C73#41semidirect
352. C8×C73C2×#41semidirect
354. #10596831C2×#41semidirect
392. C2×C73#3180semidirect
405. C2×#466D73semidirect
413. C73C2×#3180semidirect
450. #466C2×D73semidirect
649. C2×C8#11924027semidirect
751. C8C2×#11924027semidirect
789. C2#22620624direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#179891322
C2×#179891182
#226206242
C2×#179889952
C2×#179889752
C2×#179889502
C2×#179889452
C2×#179888212
C2×#179888162
C2×#179888142
C2×#179886992
C2×#179886962
C2×#179886862
C2×#179886842
C22×#145565012
C2×#466×C732
C2×#318073